“The longitudes of the stars, for 1800, have been taken from the Berlin Tables, and are those of Lacaille, Bradley, or Flamstead. The first and the last of each constellation have been taken, as well as some of the brightest of the intermediate stars. The third column indicates the year in which the longitude of the star was 0′, that is to say, that in which the star was in the equinoxial colure of spring. The last column indicates the year when the star was in the solstitial colure, whether of winter or of summer. “For Aries, Taurus, and Gemini, the winter solstice has been chosen; for the other constellations the summer solstice has been chosen, for the sake of not receding into too remote antiquity, and of not approaching too near modern times. It will be easy to find the opposite solstice, by adding the semiperiod of 12,960 years. The same rule will serve for finding the time when the star has been, or will be, at the autumnal equinox. “The sign - indicates the years before our era, the sign + the year of our era; and the last line, at the end of each sign under the title of _duration_, gives the extent of the constellation in degrees, and the time which the equinox, or the solstice, occupies in traversing the constellation from one end to the other. “The precession of 50″ yearly has been supposed, this being the result of the comparison of the catalogue of Hipparchus with the modern catalogues. We have thus the advantage of round numbers, and a general accuracy that may be relied upon. The entire period is thus 25,920 years; the semiperiod, 12,960 years; the quarter period, 6480 years; the twelfth, or a sign, 2160 years. “It is to be remarked, that the constellations leave empty spaces between them, and that sometimes they encroach upon each other. Thus, between the last star of Scorpio, and the first of Sagittarius, there is an interval of 6⅔ degrees. On the other hand, the last of Capricorn is more advanced by 14° in longitude, than the first of Aquarius. Hence, even independently of the inequality of the sun’s motion, the constellations would afford a very unequal and very erroneous measure of the year and its months. The signs of 30° furnish a more convenient and less defective one. But the signs are merely a geometrical conception; they can neither be distinguished nor observed; and they are continually changing place from the retrogradation of the equinoxial point.